Demand response is anticipated as a key feature of flexibility in renewables-dominated power systems even though high-scale aggregation and integration of demand response have never been implemented. This paper proposes a model of hourly operations during a full year of power systems integrating significant shares of demand response. Attention is given to a bottom-up description of demand response as a flexibility resource. The representation is brought up to a large-scale model of power systems through a hydropower analogy, compatible with a stochastic dual dynamic programming framework. This framework surpasses traditional stochastic dynamic programming ones as it enables the capture of intertemporal arbitrage and the effect of stochastic inputs on different timescales inherent to the operation of demand response affected by social and technical limitations. Yet, such a modeling paradigm has not permeated the study of demand response. Notably, various sources of demand response from all sectors are represented. The model is used to quantify the hypothetical economic and environmental impacts of demand response on day-ahead markets in Western Europe during 2022, a particularly tense year for this power system. Apart from the model itself, a key result is the possible misalignment between a system’s need for more flexibility sources and the private interest of an operator of demand response potentials. A cannibalization effect of demand response from the tertiary and the residential sector is also found due to the size of these potentials.